The issue I address in this thesis is the development of a relatively simple, practical algorithm, that can attenuate both specular and diffracted multiples for 2D and 3D data acquired with standard marine, narrow-azimuth towed-streamer geometry. The method uses only the recorded data and does not need costly and often inaccurate massive data interpolation and extrapolation. It does, however, require a reasonably accurate migration velocity field. The algorithm works in the image space, meaning it is applied after the data have been migrated. Since wave equation migration accurately handles complex wave propagation, the method works well for data acquired over complex subsurface regions such as under salt, again, provided the migration velocity field is reasonably accurate.
This thesis also makes theoretical contributions that explain the process by which prestack wave equation migration maps multiples from data space (CMP gathers) to image space (ADCIGs). In particular, I develop the equations that explain the residual moveout of canonical multiples in ADCIGs for both specular and diffracted multiples. I demonstrate that the specular multiples are focused similar to primaries whereas the diffracted multiples are not. For 3D data I demonstrate that the reflection azimuth dependency as a function of the dip angle is different for primaries and multiples. Likewise for the aperture angle dependency as a function of reflection azimuth. I develop a Radon transform that separates the primaries from the multiples as a function of both aperture and reflection azimuth angles.
I also develop in this thesis a new approach to the matching and adaptive subtraction of the multiple model from the data. Unlike SRME, the image space Radon transform allows the estimation of a primary model along with the estimation of the multiple model. I exploit this capability to design a nonlinear inversion approach that simultaneously matches and adaptively subtracts from the data both the estimate of the multiples and the estimate of the primaries. The effect is to reduce the well-known crosstalk problem, i.e., that residual multiple energy that contaminates the estimate of the primaries.